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The turbulent flow through a 90o pipe bend is complex with secondary flow that can affect pressure drop and heat/mass transfer. The mean and unsteady flow is studied using refractive index matched two-dimensional two-component (2D2C) Particle Image Velocimetry in a single 90o bend with Rc/D = 1.5 and at Re = 34800. The measurements were performed in a closed loop using a 1-inch diameter test section that was machined out of acrylic. The flow is imaged in the symmetric plane parallel to the axial flow and at different cross sectional planes including 0.25D and 1D upstream, 10o, 20o, 70o, 80o from the bend inlet and 0.25D and 1D downstream of the bend. The axial flow accelerates on the inner wall at the inlet and then moves towards the outer wall at 40o-50o. A shear layer is formed between high velocity fluid near the outer wall and the slower moving fluid at the inner wall side in the second half of the bend. The axial turbulent kinetic energy ((u^2 ) ̅+(v^2 ) ̅) is found to be high in regions corresponding to high velocity gradient regions: (i) at the outer wall near the inlet that extends up to the outlet, (ii) near the inner wall at 40o-50o, and (iii) at the shear layer formed near the inner wall. In the cross sectional planes, two vortices are formed and have a maximum strength at 80o from the bend inlet. The cross sectional turbulent kinetic energy ((v^2 ) ̅+(w^2 ) ̅) is found to be highest on the inner wall at the 80o plane. The snapshot Proper Orthogonal Decomposition (POD) technique is used to study the unsteady flow structures within the flow. There are long and short flow structures in the upstream pipe which can be related to Very Large Scale and Large Scale Motions. The secondary flow at 20o and further downstream cross sectional planes show evidence of unsteadiness as two vortices oscillate about the symmetry axis with low frequencies of St ~ 0.07, 0.13 and higher frequency at St ~ 0.3-0.6. The low frequency oscillations can be related to Very Large Scale Motions while high frequency oscillations are related to separation of the flow on the inner wall side. Evidence of swirl switching in the high frequency range (St ~ 0.3-0.5) is found at cross sectional plane 1D downstream. / Thesis / Master of Applied Science (MASc)

Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still encumbered by lengthy processing times. Accurate models can be produced quickly by utilizing projection Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated into a ROM. Additional sources of nonlinearities such as radiation boundary conditions, temperature dependent source heating terms, and complex geometry were also integrated. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model. / Ph. D.

In this study the complete four dimensional space time correlation function was measured in the wake of an untripped circular cylinder at a Reynolds number of 60 000. This correlation serves as the complete inflow boundary condition for an open rotor ingesting inhomogeneous turbulence. An important aspect of the turbulence ingestion problem is understanding how different inflow boundary conditions effect the sound produced by a rotor. In the present study the turbulence structure of two plane wakes were compared. Measurements completed by a previous study in the wake of a NACA 0012 airfoil were compared with the measurements completed by the present study in the wake of a cylinder. The mean flows of both plane wakes were found to be very similar, however the Reynolds stress profiles show that the cylinder wake is substantially more turbulent. The structures of the two-point correlation function in each wake are also similar, although the cylinder wake had greater maximum correlation values and was correlated at greater separations. The two-point correlation was used along with proper orthogonal decomposition to compute the average instantaneous velocity fields of both wake flows. These velocity fields represent the average eddy structures present in each wake flow. The eddy structure comparisons show that the structures in the cylinder wake are larger and better correlated at longer time delays. / Master of Science

Proper Orthogonal Decomposition (POD), combined with the Method of Snapshots and Galerkin projection, is a popular method for the model order reduction of nonlinear PDEs. The POD requires the left singular vectors from the singular value decomposition (SVD) of an n-by-m "snapshot matrix" S, each column of which represents the computed state of the system at a given time. However, the direct computation of this decomposition can be computationally expensive, particularly for snapshot matrices that are too large to fit in memory. Hierarchical Approximate POD (HAPOD) (Himpe 2016) is a recent method for the approximate truncated SVD that requires only a single pass over S, is easily parallelizable, and can be computationally cheaper than direct SVD, all while guaranteeing the requested accuracy for the resulting basis. This method processes the columns of S in blocks based on a predefined rooted tree of processors, concatenating the outputs from each stage to form the inputs for the next. However, depending on the selected parameter values and the properties of S, the performance of HAPOD may be no better than that of direct SVD. In this work, we numerically explore the parameter values and snapshot matrix properties for which HAPOD is computationally advantageous over the full SVD and compare its performance to that of a parallelized incremental SVD method (Brand 2002, Brand 2003, and Arrighi2015). In particular, in addition to the two major processor tree structures detailed in the initial publication of HAPOD (Himpe2016), we explore the viability of a new structure designed with an MPI implementation in mind. / Master of Science

Time varying flow structures are involved in a large percentage of fluid flows although there is still much unknown regarding their behavior. With the development of high spatiotemporal resolution measurement systems it is becoming more feasible to measure these complex flow structures, which in turn will lead to a better understanding of their impact. One method that has been developed for studying these flow structures is finite time Lyapunov exponents (FTLEs). These exponents can reveal regions in the fluid, referred to as Lagragnian coherent structures (LCSs), where fluid elements diverge or attract. Better knowledge of how these time varying structures behave can greatly impact a wide range of applications, from aircraft design and performance, to an improved understanding of mixing and transport in the human body. This work provides the development of new methodologies for measuring and studying three-dimensional time varying structures. Provided herein is a method to improve replacement of erroneous measurements in particle image velocimetry data, which leads to increased accuracy in the data. Also, a method for directly measuring the finite time Lyapunov exponents from particle images is developed, as well as an experimental demonstration in a three-dimensional flow field. This method takes advantage of the information inherently contained in these images to improve accuracy and reduce computational requirements. Lastly, this work provides an in depth look at the flow field for developing wall jets across a wide range of Reynolds numbers investigating the mechanisms that contribute to their development. / Ph. D.

<p dir="ltr">The Boeing-AFOSR Mach-6 Quiet Tunnel (BAM6QT) was used for a set of experiments aiming to characterize the stability regimes of stagnation point injection in noisy and quiet flow across an array of different injected gases. Four gases were used in this experiment: air, helium, carbon dioxide, and argon. These gases were injected at varying thrust coefficients, ranging from 0.0516 to 0.5666, using a 7 degree half-angle cone with a 19 mm radius spherical nose and a single 1.93 mm-radius sonic jet in the center of the model. The primary data collected consists of schlieren images gathered at a sample rate of 76 kHz. These data were then analyzed using a shock tracking software to measure the physical locations of flow features as well as through spectral proper orthogonal decomposition (SPOD) to analyze specific modes in the flow.</p><p dir="ltr">Through this analysis, it was observed that three principle modes exist in stagnation point injection regardless of the injecting gas: a high frequency vortex-coupled mode, a low frequency Mach-shock-rigid mode, and a hybrid mode residing between these two modes. The first two modes were observed in all stability regimes, whereas the hybrid mode was only observed in the bifurcated regime. Furthermore, the unsteady regime was observed to be mostly characterized by this first, vortex-coupled mode. Conversely, the steady regime was observed to be driven by the Mach-shock-rigid mode instead. This transition was measured to occur as the thrust coefficient was increased.</p><p dir="ltr">This research also found that freestream noise resulted in an amplified and widened frequency range within the Mach-shock-rigid mode. This same freestream noise did not appear to have an impact on the other two principle modes; however, in some cases the noise produced in the Mach-shock-rigid mode due to this freestream noise did in fact mask the other principle modes.</p><p dir="ltr">Lastly, it was observed that the thrust coefficient, in and of itself, is not the sole indicator of stability in stagnation point injection. Across the different injected gases in this research, transition between the stability regimes did not in fact occur at a constant thrust coefficient value. Additionally, even within the same injected gas, this transition did not occur at the same thrust coefficient value between noisy and quiet runs—indicating an effect of freestream noise on stability.</p>

With the maturity of conventional industrial robots, there has been increasing interest in designing robots that emulate realistic animal motions. This discipline requires careful and systematic investigation of a wide range of animal motions from biped, to quadruped, and even to serpentine motion of centipedes, millipedes, and snakes. Collecting optical motion capture data of such complex animal motions can be complicated for several reasons. Often there is the need to use many high-quality cameras for detailed subject tracking, and self-occlusion, loss of focus, and contrast variations challenge any imaging experiment. The problem of self-occlusion is especially pronounced for animals. In this thesis, we walk through the process of collecting motion capture data of a running lizard. In our collected raw video footage, it is difficult to make temporal correspondences using interpolation methods because of prolonged blurriness, occlusion, or the limited field of vision of our cameras. To work around this, we first make a model data set by making our best guess of the points' locations through these corruptions. Then, we randomly eclipse the data, use Gappy POD to repair the data and then see how closely it resembles the initial set, culminating in a test case where we simulate the actual corruptions we see in the raw video footage. / Master of Science